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The Effects of Turbulence on the Aerodynamics of Long-Span Bridges

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The Effects of Turbulence on the Aerodynamics of Long-Span Bridges THE EFFECTS OF TURBULENCE ON THE AERODYNAMICS OF LONG-SPAN BRIDGES A Dissertation Submitted to the Graduate School of the University of Notre Dame In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Frederick Louis Haan, Jr., B.S.E., M.S.M.E. ________________________________ Ahsan Kareem, Director ________________________________ Albin A. Szewczyk, Director Department of Aerospace and Mechanical Engineering Notre Dame, Indiana April 2000 © Copyright by Frederick L. Haan, Jr. 2000 All rights reserved THE EFFECTS OF TURBULENCE ON THE AERODYNAMICS OF LONG-SPAN BRIDGES Abstract by Frederick L. Haan, Jr. Atmospheric flows are turbulent. Experimental analysis of wind-induced vibration problems must address this issue by either matching turbulence characteristics completely or by acknowledging uncertainty in conclusions as a result of imperfect simulations. Because the former is for all practical purposes currently impossible, the latter must be understood as fully as possible. This experimental study of the effects of turbulence on long-span bridge aerodynamics examined the anatomy of turbulence effects on the self-excited forces responsible for flutter and investigated the spanwise correlation of the overall aerodynamic lift and moment. A forced-vibration technique was used with a model of rectangular cross section instrumented with 64 pressure transducers. Spanwise coherence measurements were made on both stationary and oscillating models in a series of smooth and turbulent flows. Unsteady pressure distributions were examined to observe turbulence-induced changes in the self-excited forces. This allowed a clearer understanding of turbulence Frederick L. Haan, Jr. effects than was possible by observing only integrated quantities such as flutter derivatives. For the cross section studied, turbulence stabilized the self-excited forces. Regions of maximum pressure amplitudes were observed to shift toward the leading edge with increasing turbulence intensity—similar to the behavior observed in pressure distributions on stationary bodies. This upstream shifting was responsible for the bulk of the changes in the overall stability characteristics. Spanwise correlation was quantified for both total aerodynamic forces and for self-excited and buffeting components separately. Self-excited forces showed essentially unity coherence for the entire spanwise separation range studied ( 2.4B ). This supports the assumption common in analytical estimates of fully correlated self-excited forces. It does not, however, support the hypothesis that the stabilizing effect of turbulence observed in full aeroelastic tests is due to a turbulence-induced decrease in the spanwise coherence of the self-excited forces. In the future, greater spanwise separations need to be tested for full understanding of this behavior. Spanwise correlation of the buffeting force components showed exceptional similarity between stationary and oscillating model tests. This work is dedicated to my wife Julie. No one else fully knows what went into this effort. No one else put more into it. No one else can better share with me the joy of the accomplishment. ii TABLE OF CONTENTS LIST OF FIGURES............................................................................................................ vi NOMENCLATURE.........................................................................................................xix ACKNOWLEDGEMENTS ............................................................................................xxii CHAPTER 1. INTRODUCTION........................................................................................ 1 1.1 Turbulence and Flow-Induced Vibration ............................................................. 1 1.2 Flutter of Bluff Bodies/Bridges............................................................................ 3 1.3 Aerodynamic Analysis Applied to Bridge Design Problems ............................. 10 1.4 Motivation for Study of Turbulence Effects ...................................................... 22 1.5 Outline for the rest of the dissertation................................................................ 34 CHAPTER 2. APPROACH AND BACKGROUND ....................................................... 36 2.1 The Current Approach........................................................................................ 36 2.2 Background of Bluff-Body Aerodynamics......................................................... 42 CHAPTER 3. EXPERIMENTAL SETUP........................................................................ 53 3.1 The Atmospheric Wind Tunnel.......................................................................... 53 3.2 Model ................................................................................................................. 54 3.3 Motion Driving Equipment ................................................................................ 57 3.4 Data Acquisition Equipment .............................................................................. 61 3.5 Pressure Measurements ...................................................................................... 63 3.6 Velocity Measurements...................................................................................... 64 CHAPTER 4. VELOCITY MEASUREMENTS .............................................................. 66 4.1 Summary of Incident Turbulent Flows............................................................... 66 4.2 Velocity Profiles................................................................................................. 67 4.3 Spectral Measurements ...................................................................................... 77 4.4 Correlation Measurements ................................................................................. 80 CHAPTER 5. PRESSURE FIELDS ON STATIONARY MODEL................................. 86 5.1 Summary of Pressure Analysis Methods............................................................ 86 5.2 Preliminary Tests................................................................................................ 86 5.3 Statistical Distributions of Pressure ................................................................... 91 5.4 Pressure Spectra ................................................................................................. 97 iii CHAPTER 6. PRESSURE FIELDS ON OSCILLATING MODELS—SECTION RESULTS........................................................................................................................ 106 6.1 Summary of Pressure Measurement Experiments............................................ 106 6.2 Force and Pressure Spectra............................................................................... 107 6.3 Streamwise Distributions of Amplitude and Phase.......................................... 140 6.4 Flutter Derivatives............................................................................................ 154 6.5 Aerodynamic Admittance Functions................................................................ 157 6.6 Statistical Distributions of Pressure ................................................................. 166 CHAPTER 7. SPANWISE COHERENCE AND CORRELATION RESULTS............ 178 7.1 Summary of Measurements of Spanwise Behavior.......................................... 178 7.2 Spanwise Correlation and Coherence of Forces—Stationary Model............... 178 7.3 Streamwise Position Dependence of Spanwise Pressure Correlation—Stationary Model........................................................................ 185 7.4 Spanwise Correlation and Coherence of Forces—Oscillating Model.............. 190 7.5 Streamwise Position Dependence of Spanwise Pressure Correlation—Oscillating Model....................................................................... 208 CHAPTER 8. DISCUSSION OF PRESSURE RESULTS............................................. 219 8.1 Discussion of Sectional Forces ........................................................................ 219 8.1.1 Pressure Amplitude and Phase Behavior............................................... 220 8.1.2 Flutter Derivatives ................................................................................. 226 8.1.3 Buffeting Forces on Oscillating Models................................................ 233 8.2 Discussion of Spanwise Behavior.................................................................... 234 8.2.1 Comparison of Stationary and Oscillating Model Results..................... 234 8.2.2 Comparison of Velocity and Pressure Correlation ................................ 243 8.2.3 Reduced Velocity Dependence.............................................................. 246 CHAPTER 9. CONCLUSIONS AND RECOMMENDATIONS................................... 251 9.1 Conclusions ...................................................................................................... 251 9.2 Recommendations for Future Work................................................................. 254 APPENDIX A. PRESSURE MEASUREMENT PROCEDURES................................. 257 A.1 Pressure Transducers........................................................................................ 257 A.2 Static Pressure Calibration ............................................................................... 259 A.3 Dynamic Pressure Calibration.......................................................................... 262 A.3.1 Pressure Tubing Dynamical Response..................................................
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